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Simplifying (2x + 7)(x + 1) = 28 + -2 Reorder the terms: (7 + 2x)(x + 1) = 28 + -2 Reorder the terms: (7 + 2x)(1 + x) = 28 + -2 Multiply (7 + 2x) * (1 + x) (7(1 + x) + 2x * (1 + x)) = 28 + -2 ((1 * 7 + x * 7) + 2x * (1 + x)) = 28 + -2 ((7 + 7x) + 2x * (1 + x)) = 28 + -2 (7 + 7x + (1 * 2x + x * 2x)) = 28 + -2 (7 + 7x + (2x + 2x2)) = 28 + -2 Combine like terms: 7x + 2x = 9x (7 + 9x + 2x2) = 28 + -2 Combine like terms: 28 + -2 = 26 7 + 9x + 2x2 = 26 Solving 7 + 9x + 2x2 = 26 Solving for variable 'x'. Reorder the terms: 7 + -26 + 9x + 2x2 = 26 + -26 Combine like terms: 7 + -26 = -19 -19 + 9x + 2x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -19 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 4.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 4.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 4.5x + x2 = 0 + 9.5 4.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 4.5x + x2 = 9.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 9.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 9.5 + 5.0625 Combine like terms: 9.5 + 5.0625 = 14.5625 5.0625 + 4.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 2.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 2.25 = 3.816084381 Simplifying x + 2.25 = 3.816084381 Reorder the terms: 2.25 + x = 3.816084381 Solving 2.25 + x = 3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.816084381 + -2.25 x = 3.816084381 + -2.25 Combine like terms: 3.816084381 + -2.25 = 1.566084381 x = 1.566084381 Simplifying x = 1.566084381Subproblem 2
x + 2.25 = -3.816084381 Simplifying x + 2.25 = -3.816084381 Reorder the terms: 2.25 + x = -3.816084381 Solving 2.25 + x = -3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.816084381 + -2.25 x = -3.816084381 + -2.25 Combine like terms: -3.816084381 + -2.25 = -6.066084381 x = -6.066084381 Simplifying x = -6.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.566084381, -6.066084381}
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